Luis is 2 times as old as Ashley. 30 years ago, Luis was 7 times as old as Ashley. How old is Luis now?
Solution: We can use the given information to write down two equations that describe the ages of Luis and Ashley. Let Luis's current age be $l$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $l = 2a$ 30 years ago, Luis was $l - 30$ years old, and Ashley was $a - 30$ years old. The information in the second sentence can be expressed in the following equation: $l - 30 = 7(a - 30)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = l / 2$ . Substituting this into our second equation, we get: $l - 30 = 7($ $(l / 2)$ $- 30)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $l - 30 = \dfrac{7}{2} l - 210$ Solving for $l$ , we get: $\dfrac{5}{2} l = 180$ $l = \dfrac{2}{5} \cdot 180 = 72$.